Selina Textbook Solutions: Circle: Arc and Cyclic Properties | Mathematics Class 10 ICSE PDF Download

 Page 1


Circles 
 
Exercise 17A 
Question 1. 
In the given figure, O is the centre of the circle. ?OAB and ?OCB are 30° and 40° 
respectively. Find ?AOC. Show your steps of working. 
 
 
 
Solution: 
 
Page 2


Circles 
 
Exercise 17A 
Question 1. 
In the given figure, O is the centre of the circle. ?OAB and ?OCB are 30° and 40° 
respectively. Find ?AOC. Show your steps of working. 
 
 
 
Solution: 
 
 
Question 2. 
In the given figure, ?BAD = 65°, ?ABD = 70°, ?BDC = 45° 
(i) Prove that AC is a diameter of the circle. 
(ii) Find ?ACB. 
 
 
 
Solution: 
 
 
Question 3. 
 
Given O is the centre of the circle and ?AOB = 70°. Calculate the value of: 
(i) ? OCA, 
(ii) ?OAC. 
Page 3


Circles 
 
Exercise 17A 
Question 1. 
In the given figure, O is the centre of the circle. ?OAB and ?OCB are 30° and 40° 
respectively. Find ?AOC. Show your steps of working. 
 
 
 
Solution: 
 
 
Question 2. 
In the given figure, ?BAD = 65°, ?ABD = 70°, ?BDC = 45° 
(i) Prove that AC is a diameter of the circle. 
(ii) Find ?ACB. 
 
 
 
Solution: 
 
 
Question 3. 
 
Given O is the centre of the circle and ?AOB = 70°. Calculate the value of: 
(i) ? OCA, 
(ii) ?OAC. 
 
 
Solution: 
 
Question 4. 
In each of the following figures, O is the centre of the circle. Find the values of a, b, and 
c. 
Page 4


Circles 
 
Exercise 17A 
Question 1. 
In the given figure, O is the centre of the circle. ?OAB and ?OCB are 30° and 40° 
respectively. Find ?AOC. Show your steps of working. 
 
 
 
Solution: 
 
 
Question 2. 
In the given figure, ?BAD = 65°, ?ABD = 70°, ?BDC = 45° 
(i) Prove that AC is a diameter of the circle. 
(ii) Find ?ACB. 
 
 
 
Solution: 
 
 
Question 3. 
 
Given O is the centre of the circle and ?AOB = 70°. Calculate the value of: 
(i) ? OCA, 
(ii) ?OAC. 
 
 
Solution: 
 
Question 4. 
In each of the following figures, O is the centre of the circle. Find the values of a, b, and 
c. 
 
 
Solution: 
 
 
Page 5


Circles 
 
Exercise 17A 
Question 1. 
In the given figure, O is the centre of the circle. ?OAB and ?OCB are 30° and 40° 
respectively. Find ?AOC. Show your steps of working. 
 
 
 
Solution: 
 
 
Question 2. 
In the given figure, ?BAD = 65°, ?ABD = 70°, ?BDC = 45° 
(i) Prove that AC is a diameter of the circle. 
(ii) Find ?ACB. 
 
 
 
Solution: 
 
 
Question 3. 
 
Given O is the centre of the circle and ?AOB = 70°. Calculate the value of: 
(i) ? OCA, 
(ii) ?OAC. 
 
 
Solution: 
 
Question 4. 
In each of the following figures, O is the centre of the circle. Find the values of a, b, and 
c. 
 
 
Solution: 
 
 
Question 5. 
 
In each of the following figures, O is the centre of the circle. Find the value of a, b, c and 
d. 
 
 
 
Solution: